In a mortar with a pestle, or on a cutting board using a fork, mash garlic with salt into a paste. Add anchovy fillet and continue mashing until incorporated. Scrape into a bowl and add butter, parsley, and capers. Mix well.
Spoon across a piece of plastic wrap and roll up into a 1 1/2-in.-thick log. Refrigerate at least 1 hour or up to 1 week.
With a sharp knife, cut into slices about 1/4 in. thick to top oysters.
Note: Nutritional analysis is per oyster with 1 1/2 tsp. topping.